A finite element formulation of Euler equations for the solution of steady transonic flows

Ecer, A.; Akay, H. U.

doi:10.2514/6.1982-62

Cited by 10 publications

(10 citation statements)

References 5 publications

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“…The Clebsch-type decomposition, 3 the velocity field analysis in terms of a scalar and a vector potential, 4 and the stream function formulation 5 -6 are three well-known techniques, leading to an Euler equivalent system of second-order partial differential equations solved by fast iterative algorithms. Two remarkable advantages of the stream function formulation are the fast rate of convergence (because of the existing Dirichlet boundary conditions) and that of the method being conservative; whereas the main disadvantage is the nonunique determination of the static density in terms of the mass flux.…”

Section: Introductionmentioning

confidence: 99%

Computation of rotational transonic flows using a decomposition method

1988

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Any vector field may be decomposed, in a unique way, into an irrotational and a rotational part, if appropriate boundary conditions are imposed to the scalar and vector potentials introduced by the above decomposition. In the present work, the transformation is applied to the mass flux vector, in order to calculate two-dimensional, steady, rotational, transonic flows in arbitrarily shaped ducts and plane cascades. The whole procedure is discussed from an analytical and a numerical point of view, while finite difference-finite volume schemes are used to derive numerical results. Nomenclaturea { = inlet flow angle a 2 = outlet flow angle c p -specific heat at constant pressure M = Mach number n = outward normal to the boundary vector p = pressure R g = universal gas constant S -entropy T = temperature (u,v) = velocity components in (x,y) coordinate system V = velocity vector x,y .= coordinates in physical space y = isentropic exponent £,ri = coordinates in computational space p = density O = scalar potential *p = vector potential co = relaxation factor Q = vorticity Subscripts and Superscripts t = total thermodynamic quantities n = normal to the boundary component n = number of current iteration (Note: Subscripting a variable with any of the coordinates indicates partial differentiation, whereas indices ij indicate the node point.)

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Section: Introductionmentioning

confidence: 99%

Computation of rotational transonic flows using a decomposition method

1988

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“…4 2) Development of a unified formulation for solving potential, Euler, and Navier-Stokes equations. 7 3) Development of a block-structured solution scheme for solving the steady-state flow equations through a relaxation scheme.…”

Section: Introductionmentioning

confidence: 99%

Block-structured solution scheme for analyzing three-dimensional transonic potential flows

Ecer

Spyropoulos

1987

AIAA Journal

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A block-structured solution scheme is developed for the analysis of three-dimensional transonic flows. The scheme is based on the solution of potential flow equations for individual blocks representing subvolumes of the flowfield. Based on a block-structured grid generation scheme, appropriate computational grids are generated for each of the blocks depending on the complexity of the local flowfield. The iterative scheme is designed to provide a solution of a large problem in terms of an assembly of smaller problems for each block. Numerical results illustrate the applicability of the method for analyzing flow around a NACA-0012 profile. Different block-structures are analyzed to demonstrate the robustness and the accuracy of the developed method. Finally, a three-dimensional wing-body configuration is analyzed and the results are compared with those obtained through experiments.

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“…This section describes the linearizations of the Euler equations, using a method 14) and Eq. (7.12) can be expanded to …”

Section: Linearization Of the Equationsmentioning

confidence: 99%

“…Adaptation is the process by which some aspect of the solution algorithm changes in response to an evolving solution. These changes can be in the governing equations [14], in the computational grid, or in both the equations and the grid [29]. In this thesis, adaptation refers to changes in the computational grid as the solution proceeds.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Finite Element Solution Algorithm for the Euler Equations

Shapiro¹

1991

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A new finite element algorithm for solving the steady Euler equations describing the flow of an inviscid, compressible, ideal gas is presented. This algorithm uses a finite element spatial discretization coupled with a Runge-Kutta time integration to relax to steady state. It is shown that other algorithms, such as finite difference and finite volume methods, can be derived using finite element principles. A higher-order biquadratic approximation is introduced. Several test problems are computed to verify the algorithms. Adaptive gridding in two and three dimensions using quadrilateral and hexahedral elements is developed and verified. Adaptation is shown to provide CPU savings of a factor of 2-16, and biquadratic elements are shown to provide potential savings of a factor of 2-6. An analysis of the dispersive properties of various discretization methods for the Euler equations is presented, and results allowing the prediction of dispersive errors are obtained. The adaptive algorithm is applied to the solution of several flows in scramjet inlets in two and three dimensions, demonstrating some of the varied physics associated with these flows. Some issues in the design and implementation of adaptive finite element algorithms on vector and parallel computers are discussed. Trust in the LORD with all thine heart; and lean not unto thine own understanding. In all thy ways acknowledge him, and he will direct thy paths.-Proverbs 3:5,6

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A finite element formulation of Euler equations for the solution of steady transonic flows

Cited by 10 publications

References 5 publications

Computation of rotational transonic flows using a decomposition method

Computation of rotational transonic flows using a decomposition method

Block-structured solution scheme for analyzing three-dimensional transonic potential flows

Adaptive Finite Element Solution Algorithm for the Euler Equations

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